Expressions for the periods of first- and second-kind integrals on hyperelliptic curves are given in terms of θ-constants. They are derived with the help of Thomae's classical formulae and Picard-Fuchs equations for complete integrals as functions of the parameters of the curves. The example of genus 2 is considered in detail.
|Number of pages||20|
|Journal||Philosophical Transactions A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 28 Mar 2008|